{"id":"openai-math/Schnell-fiber-spaces-and-good-canonical-models","pdf":"https://github.com/openai/math/blob/main/preprints/Schnell-fiber-spaces-and-good-canonical-models-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Schnell-fiber-spaces-and-good-canonical-models-September-24-2026","tags":["algebraic-geometry","canonical-models","kodaira-dimension"],"score":0,"title":"Schnell fiber spaces and good canonical models","domain":"Algebraic and complex geometry","family":"034","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"We prove the Campana–Peternell inequality $`\\kappa(X)\\geq\\kappa(D)`$ for a smooth connected projective complex variety X and an effective Cartier divisor D whenever $`m_0K_X-D`$ is pseudo-effective for some positive integer m 0 . For an algebraic fiber space $`f\\colon X\\to Y`$ between smooth connected projective complex varieties, the hypothesis that $`m_0K_X-f^*H`$ is pseudo-effective with H ample Cartier gives $`\\kappa(X)=\\kappa(F)+\\dim Y`$ for a very general smooth fiber F , as well as nonzero sections of $`mK_X-f^*H`$ for all sufficiently large divisible m .","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Log abundance for compact Kähler spaces under logarithmic Iitaka subadditivity"}